EASTERBROOK, Circuit Judge.

Postal inspectors detected a suspicious parcel bound from Ft. Wayne, Indiana, to Fresno, California. Wendy, a drug-detection dog, gave an alert that served as the' basis for a search warrant. The package turned out to contain $18,000 in currency and was sent on its way. The next day the inspectors came upon a package mailed in Fresno and bound for Ft. Wayne. Again Wendy alerted. A second warrant was obtained. This package contained more than four pounds of methamphetamine. Most of this was replaced by an inert lookalike but some was left for a controlled delivery; the postal inspectors added a radio transmitter that would signal the package’s location and whether it had been opened.

The drug-bearing package was addressed to Ramon Lopez at 148 E. Leidh Street in Ft. Wayne. The address was misspelled (it should have been Leith Street) and the sender’s name was fictitious. Agents obtained a third search warrant — an anticipatory authorization to enter 148 Leith St. after the delivery and opening of the package. Baltazar Ramirez signed for the parcel, using the name “Ramon Lopez.” Within minutes Ramirez left 148 E. Leith St., toting a bag large enough to contain the parcel; the radio beacon told the agents that the unopened parcel was in the bag. Ramirez walked a few blocks to 2705 S. Harrison Street, and agents followed while trying to remain hidden. One used a cell phone to call an Assistant United States Attorney to initiate the process for obtaining a fourth warrant, but during the call the agents’ receiver told them that the parcel had been opened. Whoever opened the package was bound to notice the transmitter. Fearing that the occupants would destroy evidence *797 (not only the contents of the package but also any other evidence in the house), agents entered immediately. They found Ramirez (who attempted to escape out a back door with the parcel), Luis Limares, and two women. Limares soon made in-culpatory statements. With federal agents in control of the house, others returned to the courthouse and secured the fourth search warrant. When executing that warrant agents found drugs and evidence of drug dealing in addition to the methamphetamine inside the parcel from Fresno.

After the district court denied a motion to suppress the statements made and evidence found at 2705 S. Harrison St., Ramirez and Limares pleaded guilty to possessing methamphetamine with intent to distribute that drug. Limares reserved the right to appeal the denial of the motion to suppress and was sentenced to 135 months’ imprisonment. Ramirez agreed to give up his right to appeal and cut a better deal by promising to testify against his confederates, if need be; he was sentenced to only 70 months’ imprisonment.

Limares contends that the first two warrants should not have issued because Wendy could not reliably detect drugs, and that the evidence found at 2705 S. Harrison St. must be suppressed because the agents entered before securing the fourth warrant. It is far from clear that Limares had any privacy interest in the parcels, which were not sent by or to him, so the validity of the warrants for the two parcels may be irrelevant. See Minnesota v. Carter, 525 U.S. 83, 119 S.Ct. 469, 142 L.Ed.2d 373 (1998); Rakas v. Illinois, 439 U.S. 128, 99 S.Ct. 421, 58 L.Ed.2d 387 (1978). But we need not decide whether he had some concealed interest; there is no problem with any of the searches.

According to Limares, the agents defrauded the magistrate who issued the first two search warrants by asserting that Wendy reliably detects drugs by smell. This is impossible, the argument goes, because so much currency has acquired at least some drug residue that dogs today alert more to folding money than to drugs — exemplified by what Limares calls the “false alert” to the first package, which had $18,000 in currency but no drugs. When seeking the second warrant agents told the magistrate that the first package had contained cash rather than drugs but did not add (as Limares says they should have) that this established Wendy’s unreliability. For all the magistrate knew, Li-mares asserted, Wendy alerts to anything within smelling range and thus is useless at ferreting out drugs.

The district judge held a hearing under Franks v. Delaware, 438 U.S. 154, 98 S.Ct. 2674, 57 L.Ed.2d 667 (1978), to explore the possibility that the agents had made materially false representations about Wendy’s sense of smell. He concluded that they had not done so — that Wendy can and does reliably distinguish drugs from innocuous substances. That factual finding cannot be called clearly erroneous, given its evidentiary support. According to the record, 62% of Wendy’s alerts were followed by the discovery of drugs; another 31% signaled the presence of currency. Some alerts to currency may have been false positives, but a considerable number likely resulted from currency with unusually high concentrations of drug residue, a telltale sign of money sent between drug dealers to pay for inventory. The $18,000 bound for Fresno had all the earmarks of such a shipment; people do not conduct legitimate business by mailing wads of cash hidden inside stuffed rabbits and jars of hair cream, as the sender of this package did. Only 7% of Wendy’s “hits” are unambiguous false positives, according to this record. We can’t exclude the possibility that Wendy’s success is just *798 a mirror of the agents’ ability to find drug-laden packages to put under her nose; maybe she would not fare as well on a randomly selected sample, but that possibility was not pursued at the hearing.

Limares stresses that several investigations have found that some molecules of cocaine, heroin, and other drugs can be found by sophisticated apparatus on almost all currency. This has the potential to increase the rate of false positives, and if the rate becomes high enough then dogs will no longer be able to separate drugs from innocent activities. See United States v. $506,231 in U.S. Currency, 125 F.3d 442, 453 (7th Cir.1997). It is inevitable that some molecules of drugs will adhere to every Federal Reserve note. Even a small quantity of drugs has an unimaginably large number of molecules, and these get around. A single mole of gas (which would weigh only 12 grams if all of the atoms were carbon) contains 6.02 x 1023 molecules. This implies that every living human breathes in and out, every minute, millions of oxygen and nitrogen molecules that were in George Washington’s lungs when he drew his last breath. Currency is bound to contain cocaine molecules — and for that matter some uranium and plutonium molecules too. But you can’t make an atomic bomb by combing U235 from currency that has passed through Hanford or Los Alamos. Whether you can confuse a drug-detection dog depends on how much cocaine and other drug residue clings to currency, and on how well dogs can distinguish among levels of drug residue — that is, on how dogs perform in practice, not, as Limares believes, how they were trained and “proofed off’ currency. An affidavit for a search warrant thus need not describe training methods or give the dogs’ scores on their final exams. It is enough if a dog is reliable in the field. Wendy’s handler testified that she has “never passed by anyone and suddenly done a turn for their wallet.” The affidavits in support of the two warrants said that Wendy is reliable, and the evidentiary hearing proved that out: even if all alerts to currency are treated as false positives, Wendy has been right 62% of the time, enough to prevail on a preponderance of the evidence, and “probable cause” is something less than a preponderance. See Illinois v. Gates, 462 U.S. 213, 235-36, 103 S.Ct. 2317, 76 L.Ed.2d 527 (1983); Illinois v. Wardlow, 528 U.S. 119, 124-25, 120 S.Ct. 673, 145 L.Ed.2d 570 (2000).

If the first two warrants were valid, so were the second two. But Limares was arrested, and made inculpatory statements, before the fourth warrant (authorizing the search of 2705 S. Harrison Street) had been issued. He contends that the agents violated the fourth amendment by entering 2705 S. Harrison in advance of that warrant. The district judge held otherwise, deeming the circumstances exigent because of the likelihood that drug dealers would begin to destroy evidence as soon as they saw the transmitter. Limares’s response is that the agents “created” this exigency by allowing Ramirez to walk from one building to another with the unopened package. The agents either should have arrested Ramirez before he could reach 2705 S. Harrison or should have acted more quickly to get a warrant, perhaps over the telephone, see Fed.R.Crim.P. 41(c)(2)(A), before the occupants of 2705 S. Harrison opened the package.

The first branch of this argument — that Limares had a right to have the agents arrest Ramirez before he could reach 2705 S. Harrison — runs smack into Hoffa v. United States, 385 U.S. 293, 309-10, 87 S.Ct. 408, 17 L.Ed.2d 374 (1966). Agents are not obliged to make arrests as soon as possible; they may continue investigations in order to acquire additional evi- *799 denee. If exigent circumstances intervene, the agents may act to protect that evidence from destruction. The risk that one suspect may visit an unknown place (for which the agents could not have obtained an anticipatory warrant) does not require them to halt an investigation in its tracks.

The second branch fares no better. Perhaps the agents could have moved with more dispatch to get a warrant, but they did not “manufacture” the circumstances that led to the need for haste: Ramirez did that by moving the package to a new address and then opening it while the application for a fourth warrant was being initiated. The question at hand is “not whether it was reasonable to procure a search warrant, but whether the search itself was reasonable”. United States v. Edwards, 415 U.S. 800, 806, 94 S.Ct. 1234, 39 L.Ed.2d 771 (1974), paraphrasing Cooper v. California, 386 U.S. 58, 62, 87 S.Ct. 788, 17 L.Ed.2d 730 (1967). The fourth amendment does not of its own force require a warrant for any search. Its text is a limitation on warrants (“no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized”), stemming from dissatisfaction with the use of warrants by the crown courts during colonial days. See Telford Taylor, Two Studies in Constitutional Interpretation 24-47 (1969); Akhil Reed Amar, The Constitution and Criminal Procedure: First Principles 3-17, 40-43 (1997). During the last 50 years the Supreme Court has understood the other clause of the fourth amendment (“The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated”) to require warrants in some circumstances as essential to the “reasonableness” of particularly intrusive searches, such as those into dwellings. See Chimel v. California, 395 U.S. 752, 89 S.Ct. 2034, 23 L.Ed.2d 685 (1969), overruling United States v. Rabinowitz, 339 U.S. 56, 70 S.Ct. 430, 94 L.Ed. 653 (1950), overruling Trupiano v. United States, 334 U.S. 699, 68 S.Ct. 1229, 92 L.Ed. 1663 (1948). Yet warrants are not the only way to justify entries as reasonable. Exigent circumstances are another. See, e.g., Illinois v. McArthur, 531 U.S. 326, 121 S.Ct. 946, 950, 148 L.Ed.2d 838 (2001); Warden v. Hayden, 387 U.S. 294, 298-300, 87 S.Ct. 1642, 18 L.Ed.2d 782 (1967). It was reasonable to enter and secure 2705 S. Harrison to prevent the destruction of evidence.

Agents involved in this process seem to have spent more time seeking warrants than investigating crime. They obtained four warrants all told. At oral argument Limares’s lawyer conceded that, had the agents sought a'telephonic warrant instead of cranking up the process of writing an affidavit, one was certain to have issued. We know that the magistrate issued a warrant immediately after receiving a written affidavit, and the telephonic process — which offers the judge less time to contemplate and do legal research — was bound to produce the same outcome. The agents respected the privacy of those found within 2705 S. Harrison by securing the premises but not conducting a search until the fourth warrant had been issued. This is a model of good, even over-cautious, police work; suppressing the evidence found by these agents would be a travesty. Principles such as the inevitable-discovery doctrine demonstrate the limited scope of the exclusionary rule. See Murray v. United States, 487 U.S. 533, 536-41, 108 S.Ct. 2529, 101 L.Ed.2d 472 (1988); Nix v. Williams, 467 U.S. 431, 104 S.Ct. 2501, 81 L.Ed.2d 377 (1984); United States v. Jones, 214 F.3d 836 (7th Cir.2000). But our conclusion is not that the *800 fourth warrant deprives Limares of a remedy for over-zealous action by the agents; it is that the agents acted lawfully throughout.

Affirmed.